2007/06/05 by Ram Rajagopal, Martin J. Wainwright, Rajagopal, Ram +1
Computer Science · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Information Theory (cs.IT) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.0706.0720
openalex publication_date 2007/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the following problem of decentralized statistical inference: given i.i.d. samples from an unknown distribution, estimate an arbitrary quantile subject to limits on the number of bits exchanged. We analyze a standard fusion-based architecture, in which each of m sensors transmits a single bit to the fusion center, which in turn is permitted to send some number k bits of feedback. Supposing that each of \nodenum sensors receives n observations, the optimal centralized protocol yields mean-squared error decaying as \order(1/[n m]). We develop and analyze the performance of various decentralized protocols in comparison to this centralized gold-standard. First, we describe a decentralized protocol based on k = log(\nodenum) bits of feedback that is strongly consistent, and achieves the same asymptotic MSE as the centralized optimum. Second, we describe and analyze a decentralized protocol based on only a single bit (k=1) of feedback. For step sizes independent of m, it achieves an asymptotic MSE of order \order[1/(n √(m))], whereas for step sizes decaying as 1/√(m), it achieves the same \order(1/[n m]) decay in MSE as the centralized optimum. Our theoretical results are complemented by simulations, illustrating the tradeoffs between these different protocols.